Question: Simplify to lowest terms. $\dfrac{28}{70}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 28 and 70? $28 = 2\cdot2\cdot7$ $70 = 2\cdot5\cdot7$ $\mbox{GCD}(28, 70) = 2\cdot7 = 14$ $\dfrac{28}{70} = \dfrac{2 \cdot 14}{ 5\cdot 14}$ $\hphantom{\dfrac{28}{70}} = \dfrac{2}{5} \cdot \dfrac{14}{14}$ $\hphantom{\dfrac{28}{70}} = \dfrac{2}{5} \cdot 1$ $\hphantom{\dfrac{28}{70}} = \dfrac{2}{5}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{28}{70}= \dfrac{2\cdot14}{2\cdot35}= \dfrac{2\cdot 7\cdot2}{2\cdot 7\cdot5}= \dfrac{2}{5}$